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I am afraid that is a very beginner's question, but search didn't help me (or I didn't know the terms to use).

I have a corpus of sentences which are coded for their word order (like “subject first” or “object first”). The following is an (imagined) illustration:

Sentence WordOrder
1        Subject-Object
2        Subject-IndirectObject-Object
3        Object-Subject
4        Subject-Object-IndirectObject
…        …

Frequencies:
  Subject-Object: 2.300
  Subject-IndirectObject-Object: 30
  Object-Subject: 280
  Subject-Object-IndirectObject: 560

I would like to test whether the differences in the frequency the various word order are significant. For instance, is Subject-Object significantly more common than Object-Subject?

However, I am not sure what to use, since I do not have different groups, so that a chi^2 test doesn't work (if I understand it correctly).

Is there a test for this or do I have to “construct” different groups (e.g. according to when the sentence was uttered or by whom)?

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  • $\begingroup$ Do you mean that, for example, you want to know if subject-object is less common than object-subject? $\endgroup$
    – Ian_Fin
    Aug 26 '16 at 8:12
  • $\begingroup$ @Ian_Fin Yes, exactly, sorry if that was not clear enough. I edit my question to make that clearer. $\endgroup$
    – Daniel
    Aug 26 '16 at 12:28
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The way in which I would go about approaching this would be with one way Chi-square tests. When applied to data from all four word orders this will tell you whether the there are more of any one word order than there are of any others (more specifically, does the proportion of any word order differ from .25). This is, in effect, an omnibus test.

What you're interested in is where the differences between word orders lie. In order to do this I would still use a Chi-square test, but on pairs of word orders, e.g. subject-object vs. object-subject, subject-object vs. subject-indirectobject-object. These will tell you whether there are differences in the frequencies of each pair.

Of course, you will want to apply some sort of correction to account for the inflated error rate due to the multiple comparisons, e.g. a Bonferroni correction

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  • $\begingroup$ Thanks! Do I understand it correctly that the Chi-square test you mentioned in your second paragraph is also a one way one? $\endgroup$
    – Daniel
    Aug 26 '16 at 21:34
  • $\begingroup$ @Daniel Yeah, it is. In those cases you'd be testing whether the proportion of either word order differs from .5 (i.e. is one more frequent than the other) $\endgroup$
    – Ian_Fin
    Aug 26 '16 at 21:57

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